Finite Group Databasebeta

← #11058610

Subgroups — #11058610

Order 768.

2468 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic, complemented
2C2×#5551C211yesmaximal, characteristic, complemented
3#83092C214yesmaximal, complemented
4#83028C212yesmaximal, complemented
5#82996C212yesmaximal, complemented
6#82875C214yesmaximal, complemented
7#82752C212yesmaximal, complemented
8#82666C212yesmaximal, complemented
9#82500C211yesmaximal, characteristic, complemented
10#82479C211yesmaximal, characteristic, complemented
11#82402C212yesmaximal, complemented
12#82353C212yesmaximal, complemented
13D4×C4⋊Dic3C211yesmaximal, characteristic, complemented
14#82270C212yesmaximal, complemented
15#82263C212yesmaximal, complemented
16#82076C211yesmaximal, characteristic, complemented
17C4×#930C211yesmaximal, characteristic, complemented
18#38908—31nomaximal, Sylow
19C22×#235C2212yes—
20C3×#529—28no—
21C2×C3×#126C2212yes—
22C2×C3×#125C2211yescharacteristic
23C2×C3×#124C2211yescharacteristic
24C2×C3×#123C2212yes—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×D4C2212yes—
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×#117C2212yes—
31C22×C3×C42C2211yescharacteristic
32C2×#946C2212yes—
33C2×#938C2212yes—
34C2×D4×Dic3C2212yes—
35C2×#930C2211yescharacteristic
36C2×C4×#67C2212yes—
37C22×C4⋊Dic3C2212yes—
38C2×#924C2212yes—
39C2×#924C2212yes—
40#5551—28no—
41C2×D3×C4⋊C4C2212yes—
42C2×#883C2214yes—
43C2×C4×D12C2211yescharacteristic
44C2×#869C2211yescharacteristic
45#5229C2212yes—
46#5223C2214yes—
47#5220C2214yes—
48#5213C2212yes—
49#5212C2212yes—
50#5212C2212yes—
51#5212C2211yescharacteristic
52#5212C2212yes—
53#4994C2214yes—
54#4989C2214yes—
55#4987C2214yes—
56#4987C2212yes—
57#4987C2214yes—
58#4986C2214yes—
59#4985C2214yes—
60#4984C2212yes—
61#4983C2214yes—
62#4982C2214yes—
63#4977C2212yes—
64#4959C2214yes—
65#4958C2214yes—
66#4958C2214yes—
67#4956C2214yes—
68#4952C2214yes—
69#4952C2214yes—
70#4950C2214yes—
71#4948C2214yes—
72#4942C2214yes—
73#4940C2212yes—
74#4939C2212yes—
75#4939C2211yescharacteristic
76C4×(C2×D3)⋊C4C2212yes—
77#4935C2211yescharacteristic
78C4×C4⋊Dic3C2211yescharacteristic
79#4929C2212yes—
80#4929C2212yes—
81#4929C2212yes—
82#4928C2212yes—
83#4928C2212yes—
84#4928C2211yescharacteristic
85#4928C2212yes—
86C2×#547—31no—
87C2×#529D311yescharacteristic, complemented
88#2857—31no—
89#2695—34no—
90#2693—34no—
91#2625—32no—
92#2568—31no—
93#2538—31no—
94#2535—32no—
95#2442—32no—
96#2427—32no—
97#2417—32no—
98#2417—32no—
99#2407—32no—
100D4×C4⋊C4—31no—
101#2311—32no—
102C4×#121—31no—
103C22×C3×Q8C2311yescharacteristic
104C22×C3×D4C2312yes—
105C22×C3×D4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2312yes—
110C22×#67C2314yes—
111C22×#67C2312yes—
112C23×Dic3C2314yes—
113C2×#235—28no—
114C2×#235—28no—
115C2×#235—44no—
116C22×D12C2311yescharacteristic
117C22×C4×D3C2312yes—
118C22×C4×D3C2314yes—
119C22×Dic6C2312yes—
120C3×#126—28no—
121C3×#125—24no—
122C3×#124—24no—
123C3×#123—28no—
124C3×C22⋊Q8—24no—
125C3×#121—24no—
126C3×C4×Q8—24no—
127C3×C4×D4—28no—
128C3×C4×D4D418yescomplemented
129C3×#117—28no—
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2312yes—
132C2×C3×C4⋊C4C2312yes—
133C2×C3×C4⋊C4C2312yes—
134C2×C3×C4⋊C4C2312yes—
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C22⋊C4C2312yes—
137C2×C3×C22⋊C4C2312yes—
138C2×C3×C22⋊C4C2312yes—
139C2×C3×C22⋊C4C2312yes—
140C2×C3×C22⋊C4C2312yes—
141C2×C3×C42—24no—
142C2×C3×C42C2311yescharacteristic
143C2×C3×C42C2311yescharacteristic
144C2×C3×C42C2311yescharacteristic
145C2×C3×C42C2312yes—
146C2×C3×C42C2311yescharacteristic
147C2×#217C2314yes—
148C2×#217C2312yes—
149C2×#217C2314yes—
150C2×#217C2314yes—
151#946—44no—
152#938—28no—
153D4×Dic3—44no—
154#930—24no—
155C4×#67—44no—
156C2×(C2×D3)⋊C4C2312yes—
157C2×(C2×D3)⋊C4C2312yes—
158C2×(C2×D3)⋊C4C2312yes—
159C2×(C2×D3)⋊C4C2312yes—
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yes—
162C2×C4⋊Dic3—44no—
163C2×C4⋊Dic3C2311yescharacteristic
164C2×C4⋊Dic3C2311yescharacteristic
165C2×C4⋊Dic3C2312yes—
166C2×C4⋊Dic3C2312yes—
167C2×C4⋊Dic3C2312yes—
168C2×C4⋊Dic3C2312yes—
169C2×C4⋊Dic3C2311yescharacteristic
170C2×C4⋊Dic3C2312yes—
171C2×C4⋊Dic3C2314yes—
172#924—28no—
173#924—44no—
174C2×Dic3⋊C4C2314yes—
175C2×Dic3⋊C4C2314yes—
176C2×Dic3⋊C4C2312yes—
177C2×Dic3⋊C4C2314yes—
178C2×C4×Dic3C2312yes—
179D3×C4⋊C4—28no—
180#883—216no—
181C4×D12—24no—
182#869—24no—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2312yes—
186C3⋊#95C2314yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2312yes—
192C3⋊#95C2312yes—
193C3⋊#95C2314yes—
194C22×#41—32no—
195#547—68no—
196C2×C4⋊Q8—31no—
197#529—28no—
198C2×#126C2×D312yes—
199C2×#125C2×D311yescharacteristic
200C2×#124C2×D311yescharacteristic
201C2×#123—34no—
202C2×#123C2×D312yes—
203C2×C22⋊Q8—32no—
204C2×C22⋊Q8—32no—
205C2×C22⋊Q8—32no—
206C2×C22⋊Q8C2×D311yescharacteristic
207C2×#121—32no—
208C2×#121—31no—
209C2×#121C2×D311yescharacteristic
210C2×C4×Q8C2×D311yescharacteristic
211C2×C4×D4—32no—
212C2×C4×D4—32no—
213C2×C4×D4—31no—
214C2×C4×D4C2×D312yes—
215C2×C4×D4C2×D311yescharacteristic
216C2×#117C2×D312yes—
217C22×C4⋊C4—32no—
218C22×C4⋊C4—32no—
219C22×C42C2×D311yescharacteristic
220#400—34no—
221#400—34no—
222#398—34no—
223#398—34no—
224#397—34no—
225#397—34no—
226#396—34no—
227#396—34no—
228#394—34no—
229#392—34no—
230#391—32no—
231#391—32no—
232#391—32no—
233#391—32no—
234#390—31no—
235#390—32no—
236#389—32no—
237#389—32no—
238#389—32no—
239#389—31no—
240#389—32no—
241#388—32no—
242#386—34no—
243#386—32no—
244#386—34no—
245#386—34no—
246#386—34no—
247#385—34no—
248#385—34no—
249#384—31no—
250#382—32no—
251#380—32no—
252#380—32no—
253#380—32no—
254#380—31no—
255#380—34no—
256#380—34no—
257#380—32no—
258#380—34no—
259C4×C4⋊C4—31no—
260C4×C22⋊C4—32no—
261C24×C3C2412yes—
262C24×C3C2411yescharacteristic
263C23×D3C2412yes—
264C2×C3×Q8—22no—
265C2×C3×Q8—22no—
266C2×C3×Q8—22no—
267C2×C3×D4—24no—
268C2×C3×D4—24no—
269C2×C3×D4—22no—
270C2×C3×D4—22no—
271C2×C3×D4—42no—
272C2×C3×D4C2×D414yes—
273C22×C3×C4—24no—
274C22×C3×C4—24no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—41no—
284C22×C3×C4C2×D418yes—
285C22×C3×C4C2411yescharacteristic
286C22×C3×C4C2412yes—
287C22×C3×C4C2411yescharacteristic
288C22×C3×C4C2412yes—
289C22×C3×C4C2411yescharacteristic
290C22×C3×C4C2412yes—
291C22×C3×C4C2411yescharacteristic
292C22×C3×C4C2411yescharacteristic
293C22×C3×C4C2411yescharacteristic
294C2×#67—28no—
295C2×#67—24no—
296C2×#67—24no—
297C2×#67—28no—
298C2×#67—42no—
299C2×#67—44no—
300C22×Dic3—44no—
301C22×Dic3—44no—
302C22×Dic3—44no—
303C22×Dic3C2412yes—
304C22×Dic3C2412yes—
305C22×Dic3C2414yes—
306C22×Dic3C2412yes—
307C22×Dic3C2414yes—
308#235—432no—
309C2×D12—22no—
310C2×D12—22no—
311C2×D12#4114yes—
312C2×C4×D3—28no—
313C2×C4×D3—24no—
314C2×C4×D3—28no—
315C2×C4×D3—24no—
316C2×C4×D3—24no—
317C2×C4×D3—44no—
318C2×Dic6—24no—
319C2×Dic6—24no—
320C2×Dic6—24no—
321C3×C4⋊C4—24no—
322C3×C4⋊C4—24no—
323C3×C4⋊C4—24no—
324C3×C4⋊C4—22no—
325C3×C4⋊C4—24no—
326C3×C4⋊C4C2×D414yes—
327C3×C22⋊C4—24no—
328C3×C22⋊C4—24no—
329C3×C22⋊C4—24no—
330C3×C22⋊C4—24no—
331C3×C22⋊C4C2×D418yes—
332C3×C42—22no—
333C3×C42—22no—
334C3×C42—22no—
335C3×C42—24no—
336C3×C42C2×D414yes—
337#217—28no—
338#217—44no—
339#217—42no—
340#217—44no—
341(C2×D3)⋊C4—24no—
342(C2×D3)⋊C4—24no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4—42no—
345(C2×D3)⋊C4—42no—
346(C2×D3)⋊C4—44no—
347C4⋊Dic3—24no—
348C4⋊Dic3—24no—
349C4⋊Dic3—22no—
350C4⋊Dic3—22no—
351C4⋊Dic3—24no—
352C4⋊Dic3—22no—
353C4⋊Dic3—24no—
354C4⋊Dic3—44no—
355C4⋊Dic3—42no—
356Dic3⋊C4—28no—
357Dic3⋊C4—44no—
358Dic3⋊C4—42no—
359Dic3⋊C4—44no—
360C4×Dic3—24no—
361C2×#41—68no—
362C2×#41—68no—
363C2×#41—124no—
364C22×Q8—32no—
365C22×Q8C22×D311yescharacteristic
366C22×D4—32no—
367C22×D4—34no—
368C22×D4—31no—
369C22×D4C22×D312yes—
370C22×D4C22×D311yescharacteristic
371C23×C4—34no—
372C23×C4—32no—
373C23×C4—34no—
374C23×C4C22×D311yescharacteristic
375C23×C4C22×D311yescharacteristic
376C23×C4C22×D311yescharacteristic
377C23×C4C22×D312yes—
378C4⋊Q8—64no—
379#126—28no—
380#125—24no—
381#124—24no—
382#123—28no—
383#123—616no—
384C22⋊Q8—24no—
385C22⋊Q8—68no—
386C22⋊Q8—124no—
387C22⋊Q8—124no—
388#121—24no—
389#121—64no—
390#121—68no—
391C4×Q8—24no—
392C4×D4—28no—
393C4×D4—64no—
394C4×D4—124no—
395C4×D4—124no—
396C4×D4#6718yescomplemented
397#117—28no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—32no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—32no—
408C2×C4⋊C4—34no—
409C2×C4⋊C4—34no—
410C2×C4⋊C4—32no—
411C2×C4⋊C4—68no—
412C2×C4⋊C4—124no—
413C2×C4⋊C4C22×D312yes—
414C2×C4⋊C4C22×D312yes—
415C2×C4⋊C4C22×D312yes—
416C2×C4⋊C4C22×D311yescharacteristic
417C2×C4⋊C4C22×D312yes—
418C2×C4⋊C4C22×D311yescharacteristic
419C2×C22⋊C4—34no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—32no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—32no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4C22×D312yes—
430C2×C22⋊C4C22×D312yes—
431C2×C22⋊C4C22×D312yes—
432C2×C22⋊C4C22×D312yes—
433C2×C22⋊C4C22×D312yes—
434C2×C42—24no—
435C2×C42—32no—
436C2×C42C22×D311yescharacteristic
437C2×C42C22×D312yes—
438C2×C42C22×D311yescharacteristic
439C2×C42C22×D311yescharacteristic
440C2×C42C22×D311yescharacteristic
441#95—32no—
442#95—32no—
443#95—32no—
444#95—34no—
445#95—34no—
446#95—34no—
447#95—34no—
448#95—34no—
449#95—34no—
450#95—34no—
451#95—34no—
452C23×C3—21no—
453C23×C3—22no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—22no—
457C23×C3—21no—
458C23×C3—22no—
459C23×C3—21no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—21no—
464C23×C3C22×D414yes—
465C23×C32−1+412yes—
466C23×C3C2511yescharacteristic
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3C2×#4114yes—
474C3×Q8—44no—
475C3×D4—28no—
476C3×D4—48no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—216no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—22no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—21no—
496C2×C3×C4—22no—
497C2×C3×C4—44no—
498C2×C3×C4—44no—
499C2×C3×C4—44no—
500C2×C3×C4C22×D414yes—
501C2×C3×C4C22×D412yes—
502C2×C3×C4C22×D412yes—
503C2×C3×C4C22×D412yes—
504C2×C3×C4C2×#4112yes—
505C2×C3×C4H(5,𝔽2)12yes—
506C2×C3×C4H(5,𝔽2)12yes—
507C2×C3×C42−1+412yes—
508#67—416no—
509#67—48no—
510C2×Dic3—22no—
511C2×Dic3—24no—
512C2×Dic3—22no—
513C2×Dic3—24no—
514C2×Dic3—22no—
515C2×Dic3—22no—
516C2×Dic3—22no—
517C2×Dic3—24no—
518C2×Dic3—24no—
519C2×Dic3—24no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—24no—
524C2×Dic3—22no—
525C2×Dic3—88no—
526D12—28no—
527C4×D3—416no—
528C4×D3—48no—
529Dic6—48no—
530C24—32no—
531C24C23×D311yescharacteristic
532C24C23×D312yes—
533#41—1232no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—22no—
537C2×Q8—64no—
538C2×Q8—64no—
539C2×Q8—64no—
540C2×D4—24no—
541C2×D4—24no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—34no—
545C2×D4—42no—
546C2×D4—64no—
547C2×D4—68no—
548C2×D4—64no—
549C2×D4—68no—
550C2×D4—62no—
551C2×D4—62no—
552C2×D4—122no—
553C2×D4—124no—
554C2×D4C2×#6714yes—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—32no—
566C22×C4—32no—
567C22×C4—34no—
568C22×C4—34no—
569C22×C4—32no—
570C22×C4—41no—
571C22×C4—68no—
572C22×C4—64no—
573C22×C4—64no—
574C22×C4—64no—
575C22×C4—68no—
576C22×C4—124no—
577C22×C4—124no—
578C22×C4—124no—
579C22×C4—124no—
580C22×C4C2×#6718yes—
581C22×C4C23×D311yescharacteristic
582C22×C4C23×D312yes—
583C22×C4C23×D311yescharacteristic
584C22×C4C23×D312yes—
585C22×C4C23×D311yescharacteristic
586C22×C4C23×D311yescharacteristic
587C22×C4C23×D312yes—
588C22×C4C23×D311yescharacteristic
589C22×C4C23×D311yescharacteristic
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—24no—
595C4⋊C4—62no—
596C4⋊C4—62no—
597C4⋊C4—64no—
598C4⋊C4—64no—
599C4⋊C4—64no—
600C4⋊C4—68no—
601C4⋊C4—62no—
602C4⋊C4—64no—
603C4⋊C4—124no—
604C4⋊C4—122no—
605C4⋊C4—124no—
606C4⋊C4—124no—
607C4⋊C4—122no—
608C4⋊C4C2×#6714yes—
609C22⋊C4—24no—
610C22⋊C4—24no—
611C22⋊C4—24no—
612C22⋊C4—24no—
613C22⋊C4—64no—
614C22⋊C4—68no—
615C22⋊C4—64no—
616C22⋊C4—122no—
617C22⋊C4—124no—
618C22⋊C4—122no—
619C22⋊C4—124no—
620C22⋊C4—124no—
621C22⋊C4—122no—
622C22⋊C4—124no—
623C22⋊C4C2×#6718yes—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—24no—
628C42—64no—
629C42C2×#6714yes—
630C22×C3—24no—
631C22×C3—24no—
632C22×C3—22no—
633C22×C3—24no—
634C22×C3—22no—
635C22×C3—22no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—42no—
640C22×C3—42no—
641C22×C3—42no—
642C22×C3—41no—
643C22×C3—42no—
644C22×C3C23×D411yescharacteristic
645C22×C3C22×#4111yescharacteristic
646C22×C3C2×H(5,𝔽2)11yescharacteristic
647C22×C3C2×H(5,𝔽2)11yescharacteristic
648C22×C3C2×2−1+411yescharacteristic
649C22×C3C2×2−1+411yescharacteristic
650C22×C3#58511yescharacteristic
651C2×D3—24no—
652C2×D3—24no—
653C2×D3—24no—
654C2×D3—42no—
655C2×D3—42no—
656C2×D3—42no—
657C2×D3—42no—
658C3×C4—24no—
659C3×C4—22no—
660C3×C4—41no—
661C3×C4—42no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—42no—
665C3×C4#53714yes—
666C3×C4#54614yes—
667Dic3—42no—
668Dic3—44no—
669Dic3—42no—
670Dic3—44no—
671Dic3—42no—
672C23—21no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—22no—
678C23—21no—
679C23—22no—
680C23—22no—
681C23—21no—
682C23—22no—
683C23—21no—
684C23—34no—
685C23—62no—
686C23—62no—
687C23—62no—
688C23—62no—
689C23—62no—
690C23—62no—
691C23#101012yes—
692C23C22×#6714yes—
693C23C24×D311yescharacteristic
694Q8—44no—
695Q8—128no—
696D4—28no—
697D4—48no—
698D4—68no—
699D4—1216no—
700D4—128no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—216no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—62no—
725C2×C4—64no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—64no—
729C2×C4—64no—
730C2×C4—62no—
731C2×C4—64no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—64no—
736C2×C4—62no—
737C2×C4—62no—
738C2×C4—64no—
739C2×C4—1216no—
740C2×C4—128no—
741C2×C4—248no—
742C2×C4D3×#4112yes—
743C2×C4#100912yes—
744C2×C4#100912yes—
745C2×C4#101012yes—
746C2×C4C22×#6712yes—
747C2×C4C22×#6714yes—
748C2×C4C22×#6712yes—
749C2×C4C22×#6712yes—
750C2×C3—44no—
751C2×C3—42no—
752C2×C3C2×#53711yescharacteristic
753C2×C3C2×#54611yescharacteristic
754C2×C3#348911yescharacteristic
755C2×C3#351511yescharacteristic
756C2×C3#352011yescharacteristic
757C2×C3#354611yescharacteristic
758C2×C3#355211yescharacteristic
759D3—44no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—42no—
767C22—41no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—64no—
775C22—64no—
776C22—64no—
777C22—122no—
778C22—122no—
779C22—122no—
780C22—122no—
781C22C2×D3×#4111yescharacteristic
782C22C2×#100911yescharacteristic
783C22C2×#100911yescharacteristic
784C22C2×#101011yescharacteristic
785C22C2×#101011yescharacteristic
786C22#596411yescharacteristic
787C22C23×#6711yescharacteristic
788C4—22no—
789C4—24no—
790C4—41no—
791C4—42no—
792C4—41no—
793C4—42no—
794C4—41no—
795C4—122no—
796C4—122no—
797C4—124no—
798C4—122no—
799C4—124no—
800C4#582914yes—
801C4#583314yes—
802C3#3890811yescharacteristic, complemented, Sylow
803C2—42no—
804C2—44no—
805C2—124no—
806C2#8613511yescharacteristic
807C2#8616511yescharacteristic
808C2#8616711yescharacteristic
809C2#8617411yescharacteristic
810C2#8726411yescharacteristic
811C2C2×#583311yescharacteristic
812C2C2×#582911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#529C2
hypercenterC2×#529D3
hypocenterC3#38908
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#529

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×#529C2semidirect
2. C2×#5551C2semidirect
3. #83092C2semidirect
4. #83028C2semidirect
5. #82996C2semidirect
6. #82875C2semidirect
7. #82752C2semidirect
8. #82666C2semidirect
9. #82500C2semidirect
10. #82479C2semidirect
11. #82402C2semidirect
12. #82353C2semidirect
13. D4×C4⋊Dic3C2semidirect
14. #82270C2semidirect
15. #82263C2semidirect
16. #82076C2semidirect
17. C4×#930C2semidirect
87. C2×#529D3semidirect
128. C3×C4×D4D4semidirect
396. C4×D4#67semidirect
802. C3#38908semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#5292
C2×#55512
#830922
#830282
#829962
#828752
#827522
#826662
#825002
#824792
#824022
#823532
D4×C4⋊Dic32
#822702
#822632
#820762
C4×#9302
#389083